Improved time-domain accuracy standards for model gravitational waveforms

Model gravitational waveforms must be accurate enough to be useful for detection of signals and measurement of their parameters, so appropriate accuracy standards are needed. Yet these standards should not be unnecessarily restrictive, making them impractical for the numerical and analytical modelers to meet. The work of Lindblom, Owen, and Brown [Phys. Rev. D 78, 124020 (2008)] is extended by deriving new waveform accuracy standards which are significantly less restrictive while still ensuring the quality needed for gravitational-wave data analysis. These new standards are formulated as bounds on certain norms of the time-domain waveform errors, which makes it possible to enforce them in situations where frequency-domain errors may be difficult or impossible to estimate reliably. These standards are less restrictive by about a factor of 20 than the previously published time-domain standards for detection, and up to a factor of 60 for measurement. These new standards should therefore be much easier to use effectively.

Figure 1

Curve illustrates $C_0$, the ratio of the traditional optimal signal-to-noise measure $\rho$ to a nontraditional measure defined in Eq. (11), as a function of the total mass for nonspinning equal-mass black-hole binary waveforms and for a detector with an Advanced LIGO noise curve optimized for double neutron-star binaries.

Figure 2

Curves illustrate $C_k$, the ratio of the traditional optimal signal-to-noise measure $\rho$ to a nontraditional measure defined in Eq. (18), as a function of the total mass for nonspinning equal-mass black-hole binary waveforms. The waveform accuracy standards, Eqs. (15, 16), can be enforced using any value of $k$. Thus it is sufficient to impose the standard having the largest $C_k$ in each mass range.

Figure 3

Curves illustrate the effective noise curves, $(2\pi f{)}^{2k}{S}_n(f)$, that appear in the norms of the $k$th time derivatives of the waveform. The minima of these curves are marked by the large dots. These curves illustrate why the higher time-derivative norms are more sensitive to the lower-frequency parts of the waveforms, and hence do a better job of modeling the waveform accuracy in high-mass binaries.

Figure 4

Curves show $C_{0,1}(\sigma )=\sqrt{\sigma C_0^2(M)+(1-\sigma )C_1^2(M)}$ as a function of mass for several values of the parameter $\sigma$.

Figure 5

Illustrates the allowed regions of the two-dimensional space of model-waveform errors, $({\mathcal{E}}_0,{\mathcal{E}}_1)$, satisfying various versions of the accuracy standards discussed in the text.